Library for rendering neural network NEAT
I've never used it, but, if you are using Python, have a look at neat-python, which is a Python package that implements NEAT and also provides a module, visualize, to plot the best and average fitness vs. generation, plot the change in species vs. generation, and to show the structure of a network described by a genome. See this Stack Overflow thread, if you encounter any issue while attempting to use this module. See also this example.

Have also a look at this web page, which lists links to many NEAT implementations in different languages, where some of them provide visualization tools.